The documentation lacks the information, how to exactly upgrade to 1.10.14 while the newer version is already available.
According to the PIP documentation (https://pip.pypa.io/en/stable/user_guide/#installing-packages) this should work:
python -m pip install apache-airflow==1.10.14
This seemed to work for me, but I was not able to start the websever after.
First, I had to upgrade the DB:
airflow upgradedb
Second, starting the webserver showed the problem that now the "secret_key" has to contain a real secret key.
Execute
openssl rand -hex 30
and add the hex key to the airflow.cfg file.
Then follow the remaining steps (including executing the check script) from the upgrade documentation.
As it is not described, either, the actual upgrade to 2.0 should work by using
pip install -U apache-airflow
Note especially the change in the DB upgrade command (airflow db upgrade instead of airflow upgradedb).
Regards,
HerrB92